**Hypothesis Testing Example****Objective:** Test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \).**Null Hypothesis (\( H_0 \)):** \( \mu = 55.4 \)**Alternative Hypothesis (\( H_a \)):** \( \mu < 55.4 \)**Sample Information:** You assume the population is normally distributed but the standard deviation is unknown. You collect the following sample data:- 19.2- 19.2- 76- 41**Questions:**1. **What is the test statistic for this sample?** - Provide the test statistic accurate to three decimal places.2. **What is the p-value for this sample?** - Provide the p-value accurate to four decimal places.**Decision Criteria:**- Determine if the p-value is: - Less than (or equal to) \( \alpha \) - Greater than \( \alpha \)**Conclusion:**Based on the test statistic, make a decision to either:- Reject the null hypothesis- Accept the null hypothesis- Fail to reject the null hypothesis As such, the final conclusion is that...- There is sufficient evidence to warrant rejection of the claim that the population mean is less than 55.4.- There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 55.4.- The sample data support the claim that the population mean is less than 55.4.- There is not sufficient sample evidence to support the claim that the population mean is less than 55.4.

Given that: Data points [19.2, 19.2, 76.0, 41.0] From Data points we get following: x̄= 38.85 ,s=…

Answered: You wish to test the following claim…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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You wish to test the following claim (Ha) at a significance level of a = 0.10. H.:µ = 55.4 Ha:µ < 55.4 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 19.2 19.2 76 41